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ARCHITECTURE seems to me to be the most wonderful of all the arts. We may not love it as much as others, when we are young perhaps we cannot do so, because it is so great and so grand; but at any time of life one can see that in Architecture some of the most marvellous achievements of men are displayed. The principal reason for saying this is that Architecture is not an imitative art, like Painting and Sculpture.

This book is intended essentially as an "Introduction" and does not aim at giving an exhaustive discussion of the problems with which it deals. It seemed desirable to set forth certain results, hitherto only available to those who have mastered logical symbolism, in a form offering the minimum of difficulty to the beginner. The utmost endeavour has been made to avoid dogmatism on such questions as are still open to serious doubt, and this endeavour has to some extent dominated the choice of topics considered.
The beginnings of mathematical logic are less deffinitely known than its later portions, but are of at leastequal philosophical interest. Much of what is set forth in the following chapters is not properly to be called "philosophy" though the matters concerned were included in philosophy so long as no satisfactory science of them existed.

The nature of infinity and continuity, for example, belonged in former days to philosophy, but belongs now to mathematics. Mathematical philosophy, in the strict sense, cannot, perhaps, be held to include such definite scientific results as have been obtained in this region; the philosophy of mathematics will naturally be expected to deal with questions on the frontier of knowledge, as to which comparative certainty is not yet attained.

The topics in this book are arranged for primary courses in calculus in which the formal division into differential calculus and integral calculus is deemed necessary. The book is mainly made up of matter from my Infinitesimal Calculus, Changes, however, have been made in the treatment of several topics, and some additional matter has been introduced, in particular that relating to indeterminate forms, solid geometry, and motion.
The articles on motion have been written in the belief that familiarity with the notions of velocity and acceleration, as treated by the calculus, is a great advantage to students who have to take mechanics.

“Perfect in the instant ; something went before. There must be remote matter. Nor can this remote matter suddenly Progressso from extreme unto extreme As to grow gold,and leap o'er all the means. Nature doth first beget the imperfect, then Proceeds she to the perfect.”

Philosophiæ Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy), often referred to as simply Principia, is a work in three books by Isaac Newton, in Latin, first published 5 July 1687. After annotating and correcting his personal copy of the first edition, Newton published two further editions, in 1713-1726

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In the greatly awakened interest in the common-school subjects during recent years, geography has received a large share. The establishment of chairs of geography in some of our greatest universities, the giving of college courses in physiography, meteorology, and commerce, and the general extension of geography courses in normal schools, academies, and high schools, may be cited as evidence of this growing appreciation of the importance of the subject.

While physiographic processes and resulting land forms occupy a large place in geographical control, the earth in its simple mathematical aspects should be better understood than it generally is, and mathematical geography deserves a larger place in the literature of the subject than the few pages generally given to it in our physical geographies and elementary astronomies.

A fancy overtakes us at times to question our presumption in writing a book. Wherein are we beter than another, that we should attempt to doctor another? We look over the matter-of-fact world and find it impossible to make a show, unless we have something to exhibit: Yet here are we who can fiddle little, and fife less-who cannot turn somersets, as we could once when we were less fit to write a book -who cannot commit by the page like an actor, nor play cbess witb a third-rate,-in short who cannot prove our ability by any standard feat whatsoever, proposing to indoctrinate many who can do all these things into the deepest mysteries of life!

THE AIM of this book is to exhibit the scientific connexion of the various steps by which our knowledge of the phenomena of heat has been extended. The first of these steps is the invention of the thermometer, by which the registration and comparison of temperatures is rendered possible. The second step is the measurement of quantities of heat, or Calorimetry. The whole science of heat is founded on Thermometry and Calorimetry, and when these operations are understood we may proceed to the third step, which is the investigation of those relations between the thermal and the mechanical properties of substances which form the subject of Thermodynamics.

In the monograph, which is the second in Ukraine on this topic (the first monograph - Shulga A.М. Criminal law protection of land from pollution or damage: monograph. Kharkiv: NikaNova, 2013. 256 p.)